Defining parameters
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(288\) | ||
Trace bound: | \(25\) | ||
Distinguishing \(T_p\): | \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(576, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 216 | 20 | 196 |
Cusp forms | 168 | 20 | 148 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(576, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
576.3.b.a | $4$ | $15.695$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{12}^{2}q^{5}+5\zeta_{12}q^{7}-2\zeta_{12}^{3}q^{11}+\cdots\) |
576.3.b.b | $4$ | $15.695$ | \(\Q(i, \sqrt{6})\) | \(\Q(\sqrt{-6}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{2}q^{5}-5\beta _{1}q^{7}+\beta _{3}q^{11}-71q^{25}+\cdots\) |
576.3.b.c | $4$ | $15.695$ | \(\Q(\zeta_{12})\) | \(\Q(\sqrt{-3}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{12}q^{7}+\zeta_{12}^{2}q^{13}-\zeta_{12}^{3}q^{19}+\cdots\) |
576.3.b.d | $4$ | $15.695$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{12}^{2}q^{5}+\zeta_{12}^{3}q^{7}-\zeta_{12}q^{11}+\cdots\) |
576.3.b.e | $4$ | $15.695$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{12}^{2}q^{5}-\zeta_{12}q^{7}+2\zeta_{12}^{3}q^{11}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(576, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(576, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)